Economics 423, Midterm Examination #2, Fall 2006 –
Professor Hackett
Name: ANSWER KEY [Worth one point :-) ]
4th
unit students problem 1:
Dynamically efficient allocation of a non-renewable resource:
Suppose that there are 2000
units of a nonrenewable resource available over two periods (0 and 1). Demand
in each period is given by P = 4000 - Q. Marginal cost is a constant 200 in
both periods. The discount rate is 10 percent.
1. What is the dynamically
efficient allocation of the 2000 units of the nonrenewable resource, and what
will be the prices in the two periods? (within $50 of satisfying Hotelling's
rule; show your work)
Q0 = 1133.33 P0
= 2866.67
Q1 = 866.667 P1
= 3133.33
2. Suppose that the basic
setup of the problem above were the same, except that now the discount rate
rises to 25 percent. Re-compute the dynamically efficient allocation of the
2000 units of the nonrenewable resource (within $50 of satisfying Hotelling's
rule; show your work).
Q0 = 1311.11 P0
= 2688.89
Q1 = 688.89 P1
= 3311.11
3. (a) Use the space below to
carefully draw a single fully labeled diagram correctly showing the two price
paths (for P0 and P1) over time for questions 1 and 2
immediately above. (b) Explain why one price path is steeper than the other.
Put price on the ‘Y’
axis and time on the ‘X’ axis. The price path for question 2 above is steeper
because at the higher discount rate people prefer current over future
consumption, which increases Q0 consumption and reduces Q1 consumption. Thus P0
is higher and P1 is lower.
4th unit students problem 2: The bioeconomics of a marine capture fishery:
Fishery stock = X, effort = E, stock growth is given by F(X) = aX – bX2. In a steady-state equilibrium where harvest equals stock growth, we have stock X = a/b – E/b, and harvest H = E[a/b – E/b]. Total revenue = $P * H = PE[a/b – E/b], and marginal revenue product = P[a/b – 2E/b]. Total effort cost = cE, and marginal effort cost = c.
1. (a) Derive the equation for the open-access level of effort in a steady-state equilibrium. (b) If “a” = 1000, “b” = $1, and “c” = $400, and P = $2, derive the numerical values for open-access equilibrium effort (E), stock (X), and harvest (H). Show your work:
1.a. EO = ___a-bc/P_________ (equation)
1.b. EO = ____800________ (numerical value)
XO = _____200_______ (numerical value)
HO = _____160,000_______ (numerical value)
2. (a) Derive the equation for the group-optimal level of effort in a steady-state equilibrium. (b) If “a” = 1000, “b” = $1, and “c” = $400, and P = $2, derive the numerical values for open-access equilibrium effort (E), stock (X), and harvest (H). Show your work and indicate your answer below:
2.a. E* = _____0.5*(a-bc/P)_______ (equation)
2.b. E* = _____400_______ (numerical value)
X* = ______600______ (numerical value)
H* = _____240,000_______ (numerical value)
3: Use the diagram below to carefully indicate the correct numerical equilibrium levels of harvest H (“y” axis) and stock X (“x” axis) associated with questions 1 and 2 above.
PART II. ONLY for students NOT enrolled in the 4th unit lab: There are 6 questions below. Please select any 3 of them to answer. CROSS OUT the 3 questions you do NOT want to answer. Each question is worth 10 points.
1. Carefully draw a single fully labeled diagram below correctly showing the level of environmental and natural resource law enforcement that maximizes total net benefits. Your diagram should include both a marginal benefit curve and a marginal cost curve.
See figure 9.1 in the 3rd
edition of the course textbook.
2. (i) Carefully draw a single fully labeled diagram below correctly showing Keohane's equilibrium political economy market model of effective support for legislation or administrative rules. (ii) Show how the supply or demand curve, and the equilibrium level of effective support, changes if policy makers perceive that support for this legislation will substantially improve their prospects for re-election or re-appointment.
See figure 8.1 in the 3rd
edition of the course textbook. (ii) Supply curve shifts out.
3. Suppose that proposed environmental legislation includes a provision that those who violate the law must pay a penalty equal to three times the economic gains from violating the law. It is common knowledge that 75 percent of all facilities are inspected for compliance each year, and that in recent years judges have imposed the full statutory penalty 90 percent of the time that a violation is detected. Based on this information, will the proposed legislation create deterrence (i) for risk-neutral violators, (ii) for risk-loving violators, and/or for (iii) risk-averse violators?
(i) Is the risk-neutral violator deterred? Circle one: YES NO CANNOT BE
DETERMINED
(ii) Is the risk-loving violator deterred? Circle one: YES NO CANNOT BE
DETERMINED
(iii) Is the risk-averse violator deterred? Circle one: YES NO CANNOT BE
DETERMINED
PART II. ONLY for students NOT enrolled in the 4th unit lab,
continued
4. (i) In the space
provided below, carefully draw a fully labeled diagram showing the Gordon model
of a marine capture fishery. Be sure to label all of your lines and curves.
(ii) Carefully indicate on the diagram the open access and the group optimal
levels of effort.
See figure
5.6 in the 3rd edition of your textbook.
5. (i) Re-draw the
Gordon diagram, and (using arrows or different colored lines) correctly show
how the curve(s) in the diagram will shift, and how the open access and group
optimal level of effort will change, if the price per pound of fish were to
substantially increase. (ii) In words, briefly provide an intuitive and correct
explanation for this change.
Same diagram
as above, except show that ARP and MRP curves’ ‘Y’ intercept value shifts
upwards. Reason: For given level of effort, (and for given level of fish
caught), ARP and MRP is higher.
PART II. ONLY for students NOT enrolled in the 4th unit lab,
continued
6. Suppose that there
are three firms that are capable of supplying pollution allowances – firms A,
B, and C. Suppose that each has a linear upward-sloping pollution allowance
supply curve, equal to their marginal abatement cost curve. Suppose that the
“y” intercept for firm A’s supply curve is the lowest, followed by firm B, with
firm C having the highest “y” intercept value for its allowance supply curve.
Suppose that there is a single, uniform equilibrium market price for pollution
allowances. In the space below, carefully draw a fully labeled diagram showing
each of these firms’ allowance supply curves, and clearly indicate the quantity
of allowances that each will supply at the equilibrium market price of an
allowance. Briefly explain your result.
See figure 10.3 in
the 3rd edition of your textbook. Note that at a given market price,
there is an inverse relationship between firms’ marginal abatement cost
curve/allowance supply curve and the quantity of allowances they will supply at
a given prevailing market price. This makes sense since an outward shift in a
market supply curve (i.e., a lower ‘Y’ intercept value) will induce an increase
in QS at a given market price.
Part III. ALL STUDENTS: There are 5 questions below. Please answer any 3
of them, and cross out the 2 questions you do not wish to answer with a
BIG X. Each question is worth 10 points.
1. Suppose that the marginal
benefit from reducing emissions is given by the equation MB = 200 - 3Z, and
marginal cost from reducing emissions is given by the equation MC = Z. Note
that "Z" is the percentage of total emissions to be reduced. Solve
for the percentage of total emissions reduced that maximizes total net
benefits. Show your work.
Z = ____50____ %
2. Suppose that a
risk-neutral petroleum refinery can save $10 million per year in compliance
costs by not complying with environmental regulations. Suppose that the
probability of the infraction being detected by field monitors is 50 percent,
and that the probability of a judge imposing the statutory penalty given
detection is 80 percent. If the statutory penalty calls for a fine equal to
double the annual cost savings gained by the offender, then will this system
create deterrence? Show your work.
See Chapter 9 for
details. Solve for expected penalty and compare it to the gains from violating
the law. Expected penalty = $8 million, which is < $10 million in gain.
Therefore no deterrence for risk-neutral firm.
3. Given the information in
question 2 above, what is the minimum statutory penalty that would be
just sufficient to create deterrence for this risk-neutral firm? Show your
work.
0.5 * 0.8 * X =
$10 million è X = $25 million plus $1 or so.
Minimum statutory penalty =
$_______$25 million plus $1 ________
4. Suppose that a job is
identical to many others in a competitive labor market except that there is an
additional 8 per 100,000 annual chance of accidental death, and that the job
pays a risk premium of $600 per year. Use the "value of a statistical
life" approach to determine the implied economic value of a statistical life.
Show your work.
See Chapter 7
material. VSL = $600/0.00008 = $7.5
million
VSL = $________$7.5 million ____________
Part III. ALL STUDENTS, continued
5. The data in the table
below refers to pollution emissions and marginal pollution abatement cost per
ton in an industry. Total industry-wide emissions are to be reduced by 50
percent (2400 tons/year):
|
Firms |
Historical Emissions (Tons/Yr) |
Marginal Abatement Cost
($/Ton) |
Allowances Bought |
Allowances Sold |
Total Abatement Cost (No
Tradable Allowances) |
Total Abatement Cost
(Tradable Allowances) |
|
A |
600 |
100 |
0 |
300 |
$30k |
$60k |
|
B |
600 |
200 |
0 |
300 |
$60k |
$120k |
|
C |
600 |
300 |
0 |
300 |
$90k |
$180k |
|
D |
600 |
400 |
0 |
300 |
$120k |
$240k |
|
E |
800 |
500 |
400 |
0 |
$200k |
0 |
|
F |
800 |
600 |
400 |
0 |
$240k |
0 |
|
G |
800 |
700 |
400 |
0 |
$280k |
0 |
|
TOTAL |
4,800 |
--- |
1200 |
1200 |
$1.02 mill |
$600k |
a. Suppose that the
regulatory target of cutting total emissions by 50 percent is accomplished with
a command-and-control regulatory system that requires each firm to cut its
emissions by 50 percent. Correctly fill in the "total abatement cost"
column for "no tradable allowances" in the table above.
b. Now suppose that the
regulatory target of cutting total emissions by 50 percent is accomplished by
allowing each firm to emit only 50 percent of its historical emissions. These
allowances are fully tradable. Correctly fill in the "allowances
bought", "allowances sold", and "total abatement cost,
tradable allowances" columns in the table above.
PART IV: ALL STUDENTS. Matching (13 matches, 3 points each, 39 points total). There is one uniquely correct match that connects a word or phrase on the left with a description on the right. Only clear and unambiguous answers can be marked as correct.
|
Word or Phrase |
Description |
|
a. A firm’s reputation |
1. _N_ This treaty protects the stratospheric ozone layer. |
|
b. Marginal benefit equals marginal cost |
2. _D_ Utilities can either meet renewable portfolio standard requirements by generating their own renewable energy, or by buying these from independent renewable energy generators. |
|
c. Total benefit equals total cost |
3. _A_ In order for this to generate successful self-regulation, consumers must be well-informed, have viable alternatives, and be capable of making purchase decisions based on a firm’s environmental performance that have a significant impact on the firm’s profits. |
|
d. Renewable Energy Credits |
4. _I_ Environmental valuation technique that estimates the value of non-market aspects of the environment (such as a park) that are bundled together with things (such as houses adjacent to the park) that are traded in markets. |
|
e. Firms have heterogeneous marginal abatement costs |
5. _E_ In order for cap-and-trade systems to reduce industry-wide costs of compliance, this must be true about the firms in the industry. |
|
f. Risk aversion |
6. _C_ Occurs at the level of pollution control where total net benefit equal zero. |
|
g. Risk loving |
7. _L_ Examples of these include nutrient cycling provided by wetlands, carbon absorption by trees and plankton, fruit pollination by wild insects, and water filtering provided by natural aquifers and watersheds. |
|
h. Environmental taxes |
8. _ K _ In a cap-and-trade system, the cap is designed to reduce overall pollution emissions, while the trading part is designed to do this. |
|
i. Hedonic regression method |
9. _O_ This type of regulation is subdivided into technology-based standards and uniform performance-based standards. |
|
j. Contingent valuation method |
10 _H_ Examples of these include effluent taxes on pollution emissions and excise taxes on goods made using polluting production methods. |
|
k. Reduce the industry-wide cost of regulatory compliance |
11. _F_ If the expected penalty is equal to the benefit from violating environmental or resource law, an individual with this attitude toward risk will be deterred from violating the law. |
|
l. Ecosystem services not traded in markets |
12. _G_ People with this attitude towards risk will not be deterred from environmental crime if the expected penalty equals the gain from being out of compliance |
|
m. |
13. _J_ Environmental valuation technique that estimates non-use values (existence, option, and/or bequest) associated with, say, improved wildlife habitat in a remote wilderness area. |
|
n. |
|
|
o. Command-and-control regulation |
|
|
p. The cost of pollution abatement equipment like scrubbers. |
|